Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magneti...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2008 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149000 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-149000 |
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Dorlas, T.C. Skrypnik, W.I. 2019-02-19T12:52:08Z 2019-02-19T12:52:08Z 2008 Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 82B10; 82B20; 82B26 https://nasplib.isofts.kiev.ua/handle/123456789/149000 Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magnetization in a continuous oscillator variable. The proofs use a generalized Peierls argument and two Griffiths inequalities. The class of spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States |
| spellingShingle |
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States Dorlas, T.C. Skrypnik, W.I. |
| title_short |
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States |
| title_full |
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States |
| title_fullStr |
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States |
| title_full_unstemmed |
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States |
| title_sort |
three order parameters in quantum xz spin-oscillator models with gibbsian ground states |
| author |
Dorlas, T.C. Skrypnik, W.I. |
| author_facet |
Dorlas, T.C. Skrypnik, W.I. |
| publishDate |
2008 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magnetization in a continuous oscillator variable. The proofs use a generalized Peierls argument and two Griffiths inequalities. The class of spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149000 |
| citation_txt |
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ. |
| work_keys_str_mv |
AT dorlastc threeorderparametersinquantumxzspinoscillatormodelswithgibbsiangroundstates AT skrypnikwi threeorderparametersinquantumxzspinoscillatormodelswithgibbsiangroundstates |
| first_indexed |
2025-12-07T17:29:53Z |
| last_indexed |
2025-12-07T17:29:53Z |
| _version_ |
1850871479617454080 |